The Hellenistic world had things which were similar to Buddhism and Confucianism. Confucianism is a social philosophy, and nobody can say that the Greek world didn`t have that. As for something like Buddhism, there were hundreds of Gnostic sects. Similar to India around the time when Buddhism and Jainism arose, just none of the Hellenistic ones became dominant.
I´m positive that Hellenistic and lots of other European polytheisms could have adapted to modern society. I never worked it out explicitly for Hellenistic cult, but I`ve given some thought to a possible modernised Roman religion. Some of the things I suppose could develop longevity and adaptability:
- the lares and similar animistic stuff: Catholic and Orthodox Christians have similar practices in modern societies, too (you light a candle somewhere or perform a specific gesture in some places, saying some predefined words, and expecting that something good will follow...)
- generally, I expect private cult to be more deep-rooted than public cult; people might still let a symbolic fire burn (there are Christian adaptations again) in some corner of their houses even if the government isn`t asking the haruspices anymore before bringing a law before parliament)
- as many have said, the stories about the gods were already turning into something interpreted rather symbolically
- festivities are always a good thing and very adaptable to modern society, and indeed we`re still celebrating some predominantly pagan festivities (Halloween, New Year`s Eve, summer solstice in Scandinavia) and have incorporated pagan traits into Christian festivities (Jesus` death on the cross and resurrection have nothing to do with eggs, and neither do trees and exchanges of gifts have anything to do with his birth); from the Roman religion I expect major festivities like the Parentalia and the Saturnalia could be quite popular with us modern people. As for Hellenism, I know less, but didn`t sports and theatre have some religious dimension there? That seems very modern or even postmodern to me. Sports is treated by lots of people today like something cultic, and the same applies to a lesser degree to entertaining, narrative performances or displays (think of the role your favourite TV shows play in your life)...